Generalized method of lines for first order partial functional differential equations

W. Czernous. "Generalized method of lines for first order partial functional differential equations." Annales Polonici Mathematici 89.2 (2006): 103-126. <http://eudml.org/doc/280450>.

@article{W2006,
abstract = { Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization in time of the method of lines considered in this paper leads to new difference schemes for the original problem. It is shown by examples that the new method is considerably better than the classical schemes. },
author = {W. Czernous},
journal = {Annales Polonici Mathematici},
keywords = {differential inequalities; initial boundary value problems; differential difference problems; method of lines; convergence; stability; difference schemes},
language = {eng},
number = {2},
pages = {103-126},
title = {Generalized method of lines for first order partial functional differential equations},
url = {http://eudml.org/doc/280450},
volume = {89},
year = {2006},
}

TY - JOUR
AU - W. Czernous
TI - Generalized method of lines for first order partial functional differential equations
JO - Annales Polonici Mathematici
PY - 2006
VL - 89
IS - 2
SP - 103
EP - 126
AB - Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization in time of the method of lines considered in this paper leads to new difference schemes for the original problem. It is shown by examples that the new method is considerably better than the classical schemes.
LA - eng
KW - differential inequalities; initial boundary value problems; differential difference problems; method of lines; convergence; stability; difference schemes
UR - http://eudml.org/doc/280450
ER -